$g(x)=3x-5$ $h(x)=\dfrac{2}{2x+3}$ Write $h(g(x))$ as an expression in terms of $x$. $h(g(x))=$
Answer: Let's write $g(x)$ as the input to function $h$. $h({g(x)})=\dfrac{2}{2({g(x)})+3}$ Since $g(x)=3x-5$, this becomes: $\begin{aligned} h({g(x)})&=\dfrac{2}{2({3x-5})+3}\\ &=\dfrac{2}{6x-10+3}\\ \\ &=\dfrac{2}{6x-7}\\ \\ \end{aligned}$ Note: We simplified the result to obtain a nicer expression, but this is not necessary. The answer: $h(g(x))=\dfrac{2}{6x-7}$